Memory-based prisoner's dilemma game with history optimal strategy learning promotes cooperation on interdependent networks

Cooperation is regarded as the architect of the evolution process. The research on the influence of memory mechanism on human cooperative behavior has been a hot issue in recent years. However, most previous researchers usually concentrated their efforts on the single-layer networks and the impact of memory length on cooperative behavior, but paid less attention to the interdependent networks and other factors affecting the decision-making. In this paper, we presented a two-layer interdependent Holme-Kim network model with scale-free, high clustering and interconnection characteristics and a history optimal strategy learning mechanism fully considering the historical strategy, payoffs information and memory length, and combined them to discuss the emergence and maintenance of cooperation behavior. Through modeling simulation, we studied the parameter r for network construction, memory length M and defection to temptation T. Game participants, equipped with the same memory length, played Prisoner's dilemma games with their neighbors located on home or adjacent layer (if any), and selected their following strategies for the next game round through the history optimal strategy learning mechanism. The results show that density of cooperation is inversely related to parameter r and positively related to memory length M. The newly proposed network model can improve network reciprocity and the history optimal strategy learning mechanism can find out the strategy that can bring the maximum revenue in a certain period of time. The smaller r is, the larger M is, the more conductive to cooperation.